fall back vs regress

fall back is not a noun while regress is a noun.

Word	Noun	Adjective	Verb	Adverb
fall back	No	No	Yes	No
regress	Yes	No	Yes	No

As verbs, fall back and regress are synonyms defined as:

Other synonyms of fall back include lapse, recidivate, relapse, retrogress.

As verbs, regress is a hypernym of fall back; that is, regress is a word with a broader meaning than fall back:

Other hypernyms of fall back include retrovert, return, revert, turn back.

As verbs, regress is a hypernym of fall back; that is, regress is a word with a broader meaning than fall back:

Other hypernyms of fall back include retrograde, retrogress.

fall back (noun)	regress (noun)
	returning to a former state
	the reasoning involved when you assume the conclusion is true and reason backward to the evidence

fall back (verb)	regress (verb)
go back to bad behavior	go back to bad behavior
retreat	get worse or fall back to a previous condition
hang (back) or fall (behind) in movement, progress, development, etc.	go back to a previous state
fall backwards and down	go back to a statistical means
move back and away from
have recourse to